Generalized conservation equation for multicompartmental systems

A projection operator technique is used to derive an equation for local tissue tracer content Q(t), assuming linear multicompartmental kinetics for tracer utilization. The resulting equation has the form (Equation: see text), where F and Ca(t) denote local blood flow and concentration of tracer, respectively. Tissue complexity is contained within the new parameters lambda, xi(t), and psi(t), where the time-dependent coefficients are expressed as sums of exponentials. Two simple applications are considered: tissue heterogeneity and internal trapping of tracer. The relationship to effective single compartmental analysis, as is used for local cerebral blow flow determination, is evaluated.